Vapor-dominated geothermal systems exist in a most extraordinary state: a condensate or water layer several hundred meters thick overlies a main steam zone of undetermined thickness. Why doesn't the water fall down? We show that a heavy fluid phase overlying a light phase of the same fluid in a porous medium can be stable provided the permeability in the vicinity of the interface is not too large. The special behavior of a phase change interface in response to disturbances of the boundary account for the stabilization. Heavy fluids overlying light fluids in a porous medium are unstable, irrespective of permeability, if the fluids are immiscible. Application of the stabiliy analysis to vapor-dominated geothermal systems shows that the condensate layer can be stabilized if the permeability near its base is no large than about 40 nm2 (0.04 millidarcy).